Trial lecture
Place: Auditorium 1, Helga Engs hus
Time: 10:00 - 10:45
Title: TBA
Public Defence
Place: Auditorium 1, Helga Engs hus
Time: 12:00 -
Adjudication committee
- 1st opponent: Professor Arne Jakobsen, Fakultet for utdanningsvitenskap og humaniora, University of Stavanger, Norway
- 2nd opponent: Associate Professor Charalambos Charalambous, Department of Education, University of Cyprus
- Chair of committee: Professor Marianne Ødegaard, Department of Teacher Education and School Research, University of Oslo, Norway
Chair of defence:
- Professor emeritus Magne Vestøl, Department of Teacher Education and School Research, University of Oslo, Norway
Supervisors
- Supervisor: Professor Guri Nortvedt, Department of Teacher Education and School Research, University of Oslo, Norway
- Supervisor: Professor Kirsti Klette, Department of Teacher Education and School Research, University of Oslo, Norway
Summary
The goals of mathematics education are multifaceted and can be defined in many different ways. In his 1996 work “Goals of mathematics teaching”, Mogens Niss described different levels of goals, including end, aim, and objective level goals. These levels target goals arching from broad aims of mathematics education, for instance preparing students to act as citizens in a democratic society, to gaining knowledge about mathematical processes, such as mathematical competencies, to content
goals, for example, knowing the sum of angles of a triangle. The ways in which teachers enact these goals, affect their visibility. The aim of this thesis was to explore and understand how teachers enact the three goal levels in mathematics classrooms, with a focus on Nordic lower secondary education, by using video observations, responding to the research question: What characterizes teachers’ goal enactment in Nordic mathematics classrooms? This research question was answered using three analyses, which are reported in three articles.
In the first analysis, teachers’ goal communication in the Nordic countries was investigated, with a particular focus on how goals are communicated and what goals the teachers communicate. A twostep analysis was conducted, wherein the first step included all five Nordic countries (N = 146 lessons, N = 48 classrooms), to investigate the clarity of communicated goals. In the second step, a sub-sample comprising of the Finnish, Norwegian, and Swedish video data (n = 87 lessons, n = 28 classrooms), was analyzed in-depth, to uncover what type of goals were communicated. The results showed that goal communication was characterized by vague or inferred goals. Additionally, set goals were often focused on mathematical content, and rarely on mathematical competencies or applications of mathematics.
The second analysis focused on indirect enactment of competency goals, by studying tasks applied in whole class activities and the implementation of said tasks. A targeted framework for task analysis was utilized on 323 tasks, spread across 35 lessons in Finland, Norway, and Sweden. Results indicated that a majority of tasks comprised? few opportunities for competency development. When opportunities for competency development were inherent in the tasks, they mostly comprised communication, devising strategies, and symbols and formalism competencies. In addition, these opportunities were often hidden behind large numbers of rote tasks. The analysis of the implementation indicated that teacher often reduced the inherent opportunities for competency development. Conversely, when teachers enhanced opportunities, it was mainly through the use of questioning and prompting targeting justifications, reasoning, and explanations.
In the third analysis, indirect goal enactment was explored from another perspective: contextualized mathematics. Video data from Finland, Norway, and Sweden was observed to find task sequences (N = 26), worked examples (N = 18), and offhand remarks (N = 45) where teachers’ contextualized mathematics. These were analyzed to find what contexts were introduced in the observed lessonsand what function the contexts had in relation to the mathematical ideas presented during classroom instruction. The findings showed that most contexts revolved around everyday situations such as shopping and cooking, or intra-mathematical contexts. Further, the functions of the contexts were often to provide a setting that did not impact the task solution process or the solution itself.
Overall, the thesis has two main findings: i) goals were mostly enacted indirectly, meaning that explicit goals were rare and for the most part, tasks and exemplification connected the lessons to the goals, and ii) enacted goals were most often at the objective level, which entailed that most goals comprised content, facts, and procedures, whereas aim and end level goals were rarely observable. In addition, the thesis contributes with an operationalization of Niss’ goal levels, which enables the enactment of such goals to be observed and studied